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Electricity and Magnetism

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Displacement of a Particle in a Circular Orbit

EANDM-MEV@JB

A box containing a magnetic field, pointed into the plane of the drawing, has a entrance slit in which an electron of with a velocity $v_o$ enters as shown in the accompanying figure. The velocity of the electron is perpendicular to the side of the box and to the magnetic field direction, as shown. The electron moves in a semi circle and exits the box through a exit slit that is a distance $x_o$ from the entrance slit.

If the second electron is injected at the same place as the first particle, but with twice the velocity of the first particle, what is the ratio of the new distance $x$ where it exits to the original distance, $x_o$?

A

$\cfrac{x}{x_o} =2$

B

$\cfrac{x}{x_o} =4$

C

$\cfrac{x}{x_o} =\cfrac{1}{2}$

D

$\cfrac{x}{x_o} =\cfrac{1}{4}$